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Over [174]
3 years ago
10

Find the equation of the line that passes through the point left-parenthesis 1 comma 8 right-parenthesis and is perpendicular to

the line negative startfraction 4 over 5 endfraction x plus startfraction 5 over 4 endfraction y equals negative 4.
Mathematics
1 answer:
Furkat [3]3 years ago
7 0

Don't be shy about using actual parentheses and commas.

Line through (1,8) perpendicular to    

-\dfrac 4 5 x + \dfrac 5 4 y = -4

The perpendicular family is gotten by swapping the coefficients on x and y, negating exactly one of them.   The constant is given directly by the point we're through:

\dfrac 5 4 x + \dfrac 4 5 y = \dfrac 5 4 (1) + \dfrac 4 5 (8) = \dfrac 5 4 + \dfrac{32}{5}

Let's clear the fractions by multiplying both sides by 20.

25x + 16y = 25 + 128 = 153

Might as well stop here.

Answer: 25 x + 16 y = 153


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